Question to algebraic geometers

From: utterbs <jaienviedecaca@xxxxxxxx>
Date: Mon, 22 Sep 2008 06:36:39 EDT

If S,T,U are schemes defined over an algebraically closed field k, where S--->U, T-->U are morphisms of schemes, then is S x_U T, the fibre product of S and T over U, also defined over k?

Thanks!
.

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